Nonparametric estimation of the quantiles of the conditional residual lifetime distribution

Abstract

In medical research interest is often in studying either the association between an event time T1 and a continuous covariate T2 or between two event times T1 and T2 where event times are typically subject to (right) censoring. Although the strength of dependence between such random variables can be expressed in terms of global and local association measures, it is interesting to study alternative quantities such as percentiles of the residual lifetime distribution with regard to T1, conditional on T2 taking values in a given interval. In this paper, we extend existing methods to estimate quantiles of the conditional residual lifetime distribution needed to encompass a more flexible classification of subjects into subgroups based on their respective T2-values. More specifically, we propose two estimators under one-component, respectively under univariate censoring, and provide a detailed study of their finite-sample performance. We demonstrate the use of these estimators for two medical datasets on (1) monoclonal gammopathy of undetermined significance, and (2) on overall mortality in Danish twin members.